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In these days of savage Congressional shouting matches over federal spending habits, perhaps no subject inspires louder howls than healthcare. And yet all the arguing around this budgetary bugaboo is sparked by the one conspicuous fact that everyone can agree on: In the United States, health care costs a lot.

Medicare is a particular behemoth. The health-care program for the 65-and-older crowd gobbled up roughly 13% of government spending, or $472 billion, in 2012, according to numbers from the Congressional Budget Office.

Not surprisingly, that spending isn't spread out evenly among the nearly 50 million Americans who use Medicare. New research out of Chicago Booth shows that one very large group of beneficiaries costs the government significantly more money: those who buy private, supplemental insurance known as Medigap—a curiosity of the American health insurance landscape that is available only to seniors.

Medigap is sold by health insurance giants such as United Healthcare and Mutual of Omaha, and it's hugely popular. Close to 40 percent of Medicare beneficiaries buy it. Pay a set premium, and Medigap takes the sting out of Medicare deductibles and co-pays. And seniors who are protected from that financial burden use more medical services, according to research from Booth's Neale Mahoney, an assistant professor of economics, and UT Austin's Marika Cabral.

In all, the researchers found, people with Medigap coverage cost Medicare about 22.2% more than those who don't have it. That works out to roughly $1,400 per Medigap recipient per year.

The researchers also found that in places where Medigap premiums are more expensive, fewer people opt to buy it. “People are price sensitive; for some people the price is too high,” Mahoney says. Costs for the extra coverage vary widely from state to state. And it turns out that higher prices—in other words, as the authors looked at it, a tax on Medigap premiums—could mean big savings for Medicare.

Analysis of data from across the United States revealed that a 15% tax could save the federal government $12.9 billion a year, through both the added revenue and the drop-off in people who would opt to buy extra coverage because of higher costs. If the Feds slapped on enough taxes to pay for that extra 22.2% Medigap users cost Medicare every year, Mahoney says, Medigap would essentially disappear—nobody would opt to buy it—which would translate into annual savings of $31.6 billion.

And annual savings would certainly be a boon. In 2012, Medicare costs equaled 3% of GDP, and the number of people using the program is expected only to grow in the coming decades. Yet taxing Medigap is a rather blunt instrument, Mahoney says. And confronting a hulking, complex system like Medicare likely requires something closer to a scalpel than a baseball bat, which could be a tall order in a the current political climate.

But even if policymakers did manage to agree on ways to mitigate Medigap costs to Medicare, one rather glaring question would remain: Why is it that Medigap exists in the first place?

"For every other kind of insurance you buy, you can't buy supplemental insurance to cover the gaps," Mahoney says. As an example, he pointed to another, familiar corner of the insurance market. "If you buy auto insurance, you can't buy insurance from somebody else to cover your deductible."